Geodesic
On Chebyshev's theorem and Bernoulli's law of large numbers
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 46-50

Voir la notice de l'article provenant de la source Math-Net.Ru

Using the method applyed by Chebyshev to prove the inequality that bears his name, the article provides a proof of the law of large numbers for the case of throwing the fair coin. This proof does not require familiarity with such concepts as independence, expectation, and variance. It is assumed that only the concept of equal possibility of events, the formula of classical probability, as well as the simplest concepts of combinatorics and the Newton binomial formula are known. 
@article{VMUMM_2021_3_a6,
     author = {O. P. Vinogradov},
     title = {On {Chebyshev's} theorem and {Bernoulli's} law of large numbers},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {46--50},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a6/}
}
TY  - JOUR
AU  - O. P. Vinogradov
TI  - On Chebyshev's theorem and Bernoulli's law of large numbers
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2021
SP  - 46
EP  - 50
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a6/
LA  - ru
ID  - VMUMM_2021_3_a6
ER  - 
%0 Journal Article
%A O. P. Vinogradov
%T On Chebyshev's theorem and Bernoulli's law of large numbers
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2021
%P 46-50
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a6/
%G ru
%F VMUMM_2021_3_a6
O. P. Vinogradov. On Chebyshev's theorem and Bernoulli's law of large numbers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 46-50. http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a6/